Question: Solve for $z$. Assume the equation has a solution for $z$. $-p\cdot(51+z) = dz+84$ $z=$
Explanation: The strategy Move all $z$ -terms on one side of the equation, and move all constant terms to the other side of the equation. Using the distributive property, group like terms together on both sides of the equation. To isolate $z$, divide both sides by the coefficient of $z$. Solving for $z$ $\begin{aligned} -p(51+z) &= dz+84 \\\\ -51p-pz&=dz+84&(\text{Distribute over } -p)\\\\ -51p-pz-dz &= 84 & (\text{Subtract } dz \text{ from both sides}) \\\\ -pz-dz&=84+51p&(\text{Add } 51p \text{ to both sides})\\\\ z(-p-d) &= 84+51p & (\text{Factor out }z) \\\\ z &= \dfrac{84+51p}{-p-d} & (\text{Divide both sides by } -p-d)\end{aligned}$ [Is it OK to divide by an unknown quantity?] The answer $z = \dfrac{84+51p}{-p-d} $